Rhythmogenesis in the sinoatrial unit of the heart

The most significant experimental data about the formation of a uniform rhythm of the sinoatrial unit of the heart for both the intact sinoatrial unit of the heart and cardiomyocytes in cellular structures are presented. The basic mathematical models for studying the processes of synchronization in the sinoatrial unit of the heart are described, including equations of Noble, Bonhoffer, and van der Pol and modified axiomatic models. The basic results obtained using the mathematical models are presented. The major reasons influencing the formation of a uniform rhythm were revealed: the form of a potential pacemaker in the phase of slow diastolic depolarization, its porosity, the force of connection between pacemaker and electric capacity of pacemakers. A study of rhythmogenisis on the basis of the modified axiomatic model was carrud out. The method allows one to calculate the uniform rhythm of the sinoatrial unit of the heart in view of the mutual influence of pacemaker cells, including the force of connection, electric capacity of cells, their possible clusterization. It was shown that generally the uniform rhythm of the sinoatrial unit of the heart is formed on an intermediate level of all pacemaker cells.     

A mechanism for setting a single rhythm for a multipacemaker sinoatrial node

Interaction of the system of n pacemaker cells modelling the work of the heart sinoatrial node was studied. Suggesting the interaction additivity an expression was obtained for the system single rhythm. Dependence of the system single rhythm and propagation velocity of excitation delay on the number of pacemakers of the leading centre and connection force between the pacemakers was investigated. The results obtained qualitatively, agree with the experimental evidence available.     

Investigation of the synchronization of the sinoatrial node upon stimulation from atria

The excitation of the sinoatrial node from frog heart atria has been experimentally investigated. Potentials were measured by means of microelectrodes introduced in pacemaker cells of the sinoatrial node. It has been found that atria can modulate the rhythm of the sinoatrial node due to electric and electromechanical actions, among which the electromechanical action is more important. Specific transient processes accompanying the establishment of the stationary rhythm have been studied. A mathematical model of the transient processes of achieving the rhythm of the sinoatrial node is proposed on the basis of Diophantine methods. The calculations performed using the mathematical model satisfactorily agree with the experimental results. The stabilizing role of atria in forming the rhythm of the sinoatrial node is revealed.     

用生物学方法重建心脏起搏点的研究进展

正常人的心脏节律源于右心房的天然起搏点（pacemaker）——窦房结。窦房结的功能异常或者房室传导阻滞会导致心率异常（如心律缓慢）。治疗严重的心动过缓需要植入在技术上已经相当成熟的电子起搏器,但这种治疗存在一些缺陷和不足。近年来,在动物实验模型中应用基因或细胞来重建心脏的生物起搏点已经取得了进展。超极化活化环核苷酸门控（hyperpolarization-activated cyclic-nucleotide-modulated,HCN）通道（起搏通道）通过超极化活化的阳离子电流（hyperpolarization-activated cation current,It）调制心脏的自律性。利用病毒载体或转染HCN基因的细胞将HCN基因导入动物心脏内可重建生物起搏点。也有导入其它基因或植入自律细胞来探索心脏起搏点的重建。本文总结了重建心脏生物起搏点的一些研究进展。一旦稳定性和寿命等关键问题得到相应解决,遗传工程改造的生物起搏点可用于治疗严重的心动过缓。     

The mechanism of setting the common rhythm of the pacemaker pair in the sinoatrial node

Principal physiological hypotheses concerning the setting of united rhythm in the heart sinoatrial node (SAN) are considered. A mathematical model of SAN is proposed which takes into account properties of individual elementary pacemakers and their interaction. Assuming paired interaction of the pacemakers there are revealed the main P.D. parameters, affecting the setting of the united rhythm. Quantitative expressions are obtained for the united rhythm period, delay and propagation velocity of the excitation. The calculated data are compared with the experimental ones. The hypothesis concerning the setting of the united rhythm as a result of the interaction of SAN pacemakers is confirmed.     

A study of synchronization of the sinus unit upon stimulation from auricles

The excitation of the sinoatrial unit from heart auricles of the frog has been studied. Potentials were recorded by means of microelectrodes inserted to pacemaker of the sinoatrial unit. It has been established that auricles can impart the rhythm to the sinoatrial unit due to electric and electromechanical influence, and electromechanical influence is of greater significance. Specific transitions accompanying the establishment of the stationary rhythm have been studied. A mathematical model of transitions of the establishment of the rhythm of the sinoatrial unit, which is based on diophant methods is offered. The catculations performed by means of the mathematical model coincide well with results of experimental studies. The stabilizing role of auricles in the formation of the rhythm of the sinoatrial unit has been established.     

Bifurcation analysis and effects of changing ionic conductances on pacemaker rhythm in a sinoatrial node cell model

The electrical excitation (action potential generation) of sinoatrial node (cardiac pacemaker) cells is directly related to various ion channels (pore-forming proteins) in cell membranes. In order to analyze the relation between action potential generation and ion channels, we use the Yanagihara-Noma-Irisawa (YNI) model of sinoatrial node cells, which is described by the Hodgkin-Huxley-type equations with seven variables. In this paper, we analyze the global bifurcation structure of the YNI model by varying various conductances of ion channels, and examine the effects of these conductance changes on pacemaker rhythm (frequency of action potential generation). The coupling effect on pacemaker rhythm is also examined approximately by applying external current to the YNI model.     

The effects of intracellular calcium dynamics on the electrical activity of the cells of the sinoatrial node

We studied the effects of intracellular calcium dynamics on the spontaneous activity of the pacemaker cells using mathematical modeling. We compared the responses to the suppression of L-type calcium currents in several models of the electrical activity of cells of the sinoatrial node. All models showed a decrease in the maximum depolarization rate, the amplitude of action potentials, and the duration of the action potential. The model of the calcium clock showed an increase in the oscillation period by 12%. Models with the spontaneous activity, which is determined by the current activated by hyperpolarization, showed a decrease of the oscillation period by 15%. The comparison of the theoretic results with the experimental data showed that intracellular mechanisms had a different input in the spontaneous activity of pacemakers in the center and periphery of the sinoatrial node.     

Simulation analysis of excitation conduction in the heart: Propagation of excitation in different tissues

The normal excitation and conduction in the heart are maintained by the coordination between the dynamics of ionic conductance of each cell and the electrical coupling between cells. To examine functional roles of these two factors, we proposed a spatially-discrete model of conduction of excitation in which the individual cells were assumed isopotential. This approximation was reasoned by comparing the apparent space constant with the measured junctional resistance between myocardial cells. We used the four reconstruction models previously reported for five kinds of myocardial cells. Coupling coefficients between adjacent cells were determined quantitatively from the apparent space constants. We first investigated to what extent the pacemaker activity of the sinoatrial node depends on the number and the coupling coefficient of its cells, by using a one-dimensional model system composed of the sinoatrial node cells and the atrial cells. Extensive computer simulation revealed the following two conditions for the pacemaker activity of the sinoatrial node. The number of the sinoatrial node cells and their coupling coefficients must be large enough to provide the atrium with the sufficient electric current flow. The number of the sinoatrial node cells must be large so that the period of the compound system is close to the intrinsic period of the sinoatrial node cell. In this simulation the same sinoatrial node cells produced action potentials of different shapes depending on where they were located in the sinoatrial node. Therefore it seems premature to classify the myocardial cells only from their waveforms obtained by electrical recordings in the compound tissue. Second, we investigated the very slow conduction in the atrioventricular node compared to, for example, the ventricle. This was assumed to be due to the inherent property of the membrane dynamics of the atrioventricular node cell, or to the small value of the coupling coefficient (weak intercellular coupling), or to the electrical load imposed on the atrioventricular node by the Purkinje fibers, because the relatively small atrioventricular node must provide the Purkinje fibers with sufficient electric current flow. Relative contributions of these three factors to the slow conduction were evaluated using the model system composed of only the atrioventricular cells or that composed of the atrioventricular and Purkinje cells. We found that the weak coupling has the strongest effect. In the model system composed of the atrioventricular cells, the propagation failure was not observed even for very small values of the coupling coefficient.(ABSTRACT TRUNCATED AT 400 WORDS)     

Model of bidirectional interaction between myocardial pacemakers based on the phase response curve

As a basis for the study of sinus rhythm determination, a model is proposed of bidirectionally-coupled oscillators as a system of difference equations based on the phase response curve of sinoatrial pacemaker cells. Solutions corresponding to the one-to-one synchronization of the two pacemakers are obtained, and the relation among those solutions is examined: It is revealed that two different solutions with different cycle length coexist, and the synchronized frequency can be higher or lower than the original intrinsic frequencies of the two pacemaker cells. The experimental results of the cultured cells of cardiac pacemakers are interpreted by the analytical result of the model.     

To the formation of a unified rhythm in the heart sinoatrial node

The dynamics of establishing a unified sinoatrial node rhythm are considered. Mutual synchronization is shown to result in phase shifts and excitation delays. Rhythmogenesis in systems of two or many interacting pacemaker cells is examined in several point models and distributed models (Noble, Bonhoeffer-van der Pol, FitzHugh, Hodgkin-Huxley, Morris-Lecar).     

Beating irregularity of single pacemaker cells isolated from the rabbit sinoatrial node.

Single pacemaker heart cells discharge irregularly. Data on fluctuations in interbeat interval of single pacemaker cells isolated from the rabbit sinoatrial node are presented. The coefficient of variation of the interbeat interval is quite small, approximately 2%, even though the coefficient of variation of diastolic depolarization rate is approximately 15%. It has been hypothesized that random fluctuations in interbeat interval arise from the stochastic behavior of the membrane ionic channels. To test this hypothesis, we constructed a single channel model of a single pacemaker cell isolated from the rabbit sinoatrial node, i.e., a model into which the stochastic open-close kinetics of the individual membrane ionic channels are incorporated. Single channel conductances as well as single channel open and closed lifetimes are based on experimental data from whole cell and single channel experiments that have been published in the past decade. Fluctuations in action potential parameters of the model cell are compared with those observed experimentally. It is concluded that fluctuations in interbeat interval of single sinoatrial node pacemaker cells indeed are due to the stochastic open-close kinetics of the membrane ionic channels.     

Pacemaker activity of the rabbit sinoatrial node. A comparison of mathematical models.

In the past decade, three mathematical models describing the pacemaker activity of the rabbit sinoatrial node have been developed: the Bristow-Clark model, the Irisawa-Noma model, and the Noble-Noble model. In a comparative study it is demonstrated that these models, as well as subsequent modifications, all have several drawbacks. A more accurate model, describing the pacemaker activity of a single pacemaker cell isolated from the rabbit sinoatrial node, was constructed. Model equations, including equations for the T-type calcium current, are based on experimental data from voltage clamp experiments on single cells that were published during the last few years. In contrast to the other models, only a small amount of background current contributes to the overall electrical charge flow. The action potential parameters of the model cell, its responses to voltage clamp steps and its current-voltage relationships have been computed. The model is used to discuss the relative contribution of membrane current components to the slow diastolic depolarization phase of the action potential.     

Computer simulation of the preautomatic pause in pacemaker cells of the sinoatrial node

The duration of the preautomatic pause as a function of sinoatrial node, the type of pacemaker cells, acetylcholine concentration, the duration of high-frequency stimulation, and the conductivity of gap junctions has been studied. It was found that the preautomatic pause in peripheral pacemakers occurs at a higher concentration of acetylcholine as compared with central pacemakers. The dependence of the duration of the preautomatic pause on the gap junction conductivity is a nonlinear one.     

Interbeat Interval Modulation in the Sinoatrial Node as a Result of Membrane Current Stochasticity—A Theoretical and Numerical Study

A single isolated sinoatrial pacemaker cell presents intrinsic interbeat interval (IBI) variability that is believed to result from the stochastic characteristics of the opening and closing processes of membrane ion channels. To our knowledge, a novel mathematical framework was developed in this work to address the effect of current fluctuations on the IBIs of sinoatrial pacemaker cells. Using statistical modeling and employing the Fokker-Planck formalism, our mathematical analysis suggests that increased stochastic current fluctuation variance linearly increases the slope of phase-4 depolarization, hence the rate of activations. Single-cell and two-dimensional computerized numerical modeling of the sinoatrial node was conducted to validate the theoretical predictions using established ionic kinetics of the rabbit pacemaker and atrial cells. Our models also provide, to our knowledge, a novel complementary or alternative explanation to recent experimental observations showing a strong reduction in the mean IBI of Cx30 deficient mice in comparison to wild-types, not fully explicable by the effects of intercellular decoupling.     

Minor contribution of cytosolic Ca2+ transients to the pacemaker rhythm in guinea pig sinoatrial node cells

The question of the extent to which cytosolic Ca(2+) affects sinoatrial node pacemaker activity has been discussed for decades. We examined this issue by analyzing two mathematical pacemaker models, based on the "Ca(2+) clock" (C) and "membrane clock" (M) hypotheses, together with patch-clamp experiments in isolated guinea pig sinoatrial node cells. By applying lead potential analysis to the models, the C mechanism, which is dependent on potentiation of Na(+)/Ca(2+) exchange current via spontaneous Ca(2+) release from the sarcoplasmic reticulum (SR) during diastole, was found to overlap M mechanisms in the C model. Rapid suppression of pacemaker rhythm was observed in the C model by chelating intracellular Ca(2+), whereas the M model was unaffected. Experimental rupturing of the perforated-patch membrane to allow rapid equilibration of the cytosol with 10 mM BAPTA pipette solution, however, failed to decrease the rate of spontaneous action potential within ～30 s, whereas contraction ceased within ～3 s. The spontaneous rhythm also remained intact within a few minutes when SR Ca(2+) dynamics were acutely disrupted using high doses of SR blockers. These experimental results suggested that rapid disruption of normal Ca(2+) dynamics would not markedly affect spontaneous activity. Experimental prolongation of the action potentials, as well as slowing of the Ca(2+)-mediated inactivation of the L-type Ca(2+) currents induced by BAPTA, were well explained by assuming Ca(2+) chelation, even in the proximity of the channel pore in addition to the bulk cytosol in the M model. Taken together, the experimental and model findings strongly suggest that the C mechanism explicitly described by the C model can hardly be applied to guinea pig sinoatrial node cells. The possible involvement of L-type Ca(2+) current rundown induced secondarily through inhibition of Ca(2+)/calmodulin kinase II and/or Ca(2+)-stimulated adenylyl cyclase was discussed as underlying the disruption of spontaneous activity after prolonged intracellular Ca(2+) concentration reduction for >5 min.     

Conduction barriers and pathways of the sinoatrial pacemaker complex: their role in normal rhythm and atrial arrhythmias

Since Keith and Flack's anatomical discovery of the sinoatrial node (SAN), the primary pacemaker of the heart, the question of how such a small SAN structure can pace the entire heart has remained for a large part unanswered. Recent advances in optical mapping technology have made it possible to unambiguously resolve the origin of excitation and conduction within the animal and human SAN. The combination of high-resolution optical mapping and histological structural analysis reveals that the canine and human SANs are functionally insulated from the surrounding atrial myocardium, except for several critical conduction pathways. Indeed, the SAN as a leading pacemaker requires anatomical (fibrosis, fat, and blood vessels) and/or functional barriers (paucity of connexins) to protect it from the hyperpolarizing influence of the surrounding atrium. The presence of conduction barriers and pathways may help explain how a small cluster of pacemaker cells in the SAN pacemaker complex manages to depolarize different, widely distributed areas of the right atria as evidenced functionally by exit points and breakthroughs. The autonomic nervous system and humoral factors can further regulate conduction through these pathways, affecting pacemaker automaticity and ultimately heart rate. Moreover, the conduction barriers and multiple pathways can form substrates for reentrant activity and thus lead to atrial flutter and fibrillation. This review aims to provide new insight into the function of the SAN pacemaker complex and the interaction between the atrial pacemakers and the surrounding atrial myocardium not only in animal models but also human hearts.     

A view of the cardiac rhythm control: Intrinsic regulation

Regulation of the cardiac rhythm is intricate and occurs at least at two major levels, intrinsic and extrinsic. In turn, each of these levels can be divided into several sublevels. The factors regulating the cardiac activity eventually affect the duration of spontaneous diastolic depolarization of pacemaker myocytes of the sinoatrial node and, to a far lesser extent, the conduction velocity in the conduction system of the heart. Intrinsic regulation of the heart rate (HR) includes the myogenic sublevel and the sublevels of cell-to-cell communication, the cardiac nervous system, and humoral factors produced within the heart. Myogenic regulation is considered to be the first sublevel in control of the cardiac function. The available data suggest myogenic regulation only for the contractility of the myocardium. The cell-to-cell regulation sublevel involves two principal mechanisms. One depends on the heterogeneous structure of the sinoatrial node and within-node shifts of the dominant pacemaker, which is a group of cells that determine the HR and govern all other cells of the sinoatrial node. The other mechanism is based on the effects of peptides produced by cardiomyocytes and endothelial cells on pacemaker cells of the sinoatrial node. Regulatory peptides are also produced by the cardiac nervous system, which includes sensory and effector autonomic fibers, represents the cardiac part of the metasympathetic system, and forms intramural ganglia. In addition to modulating the HR, these peptides affect the contractility, microcirculation, coronary blood flow, preload, and afterload. Currently available data demonstrate that the autonomic nervous system is far more intricate than believed earlier. Using various neuropeptides, this system provides for fine adjustment of the cell functions, subject to its immediate control.Translated from Fiziologiya Cheloveka, Vol. 31, No. 2, 2005, pp. 116–129.Original Russian Text Copyright © 2005 by Nozdrachev, Kotelnikov, Mazhara, Naumov.Deceased.     

Organization and development of pacemaker of the gastrointestinal tract

Rhythmical depolarization and automatic contractions of smooth musculature of the gastrointestinal tract are a consequence of pacemaker activity of c-Kit-immunoreactive cells of mesenchymal origin—interstitial Cajal cells (ICC) that have a peculiar mechanism of intercellular Ca²⁺ balance, which is controlled by mitochondria. Intermuscular layer cells (ICC-MY) generate pacemaker potentials. Their induced depolarization is enhanced by unitary potentials generated by intracellular population—ICC-IM. Summation of unitary potentials in the tact of the pacemaker ones leads to creation of the second potential of slow waves—plateau potentials. Due to the presence of synapse-like structures, ICC serve messenger of transmission of the enteral nervous system onto the muscle. Long processes and close intercellular contacts similar to tight junction provide conductance and coordination of excitation in the intestinal musculature. Electrical rhythmicity appears in the intestinal muscle at the prenatal development period in parallel with the structural and functional ICC maturation, but establishment of mature rhythm parameters occurs in early postnatal ontogenesis. Features of similarity and difference in organization of control by pacemakers of the heart and musculature of the gastrointestinal tract are discussed.